First, the transformation method:

Transforming thinking is both a method and a kind of thinking. Transformational thinking refers to changing the direction of the problem from one form to another from different angles when encountering obstacles in the process of solving problems, and seeking the best way to make the problem simpler and clearer.

Second, the logical method:

Logic is the foundation of all thinking. Logical thinking is a thinking process in which people observe, compare, analyze, synthesize, abstract, generalize, judge and reason things with the help of concepts, judgments and reasoning in the process of cognition. Logical thinking is widely used to solve logical reasoning problems.

Third, the reverse method:

Reverse thinking, also known as divergent thinking, is a way of thinking about common things or opinions that seem to have become conclusive. Dare to "do the opposite", let thinking develop in the opposite direction, conduct in-depth exploration from the opposite side of the problem, establish new concepts and shape new images.

Fourth, the corresponding method:

Corresponding thinking is a way of thinking that establishes a direct connection between quantitative relations (including quantity difference, quantity times and quantity rate). General correspondence (such as the sum and difference times of two or more quantities) and ratio correspondence are more common.

Verb (abbreviation of verb) is an innovative method;

Innovative thinking refers to the thinking process of solving problems with novel and original methods. Through this kind of thinking, we can break through the boundaries of conventional thinking, think about problems with unconventional or even unconventional methods and perspectives, and come up with unique solutions. It can be divided into four types: difference type, exploration type, optimization type and negative type.

Click to view: the core concepts and thinking methods of learning mathematics well.

Six, the system method:

Systematic thinking is also called holistic thinking. Systematic thinking refers to having a systematic understanding of the knowledge points involved in a specific topic when solving a problem, that is, analyzing and judging what the knowledge points belong to when getting the topic, and then recalling what types of such questions are divided into and the corresponding solutions.

Seven, analogy method:

Analogical thinking refers to the thinking method of comparing unfamiliar and unfamiliar problems with familiar problems or other things according to some similar properties between things, discovering the essence of knowledge, finding its essence, and thus solving problems.

Eight, mirror method:

Thinking in images mainly refers to people's choice of images in the process of understanding the world, and refers to the thinking method of solving problems with intuitive images. Imagination is the advanced form and basic method of thinking in images.

2. How to exercise your mathematical thinking?

First, it is better to say it than to do it, and it is better to make sense than to understand it.

To do 10, let's say one. After the children finish their homework, parents may wish to encourage them to explain the difficult problems in math homework. I will often send some good training questions in the group, and you can also encourage them to think about it. If they speak well, parents can also give small rewards to make their children feel more fulfilled.

Second, learn to draw inferences from others and be flexible.

The metaphor comes from Confucius' The Analects of Confucius: "It is enough to take a corner and not use three corners instead." I'll name one corner, and you should be able to think of the other three corners flexibly. If not, I won't teach you any more. Later, everyone changed this passage of Confucius into the idiom "draw inferences from one instance", which means that when you learn one thing, you can think flexibly and apply it to other similar things!

In the training of mathematics, we must give the children inferences. A problem seems to be understood, but his thinking may be straight, and he still can't turn around without doing a few questions that are extrapolated or modified on this basis.

Inference is actually the execution behavior of the sentence "the master leads the door and learns the art in himself".

Third, establish a wrong book and cultivate correct thinking habits.

Every time I have the first class, the content of the course I talk about is related to the students' wrong questions. I usually extract several typical questions from the wrong questions in the test paper and tell them again in class as examples. The students' reaction is either unfamiliar with the topic or very familiar with it, but they have no ideas. The occurrence of these phenomena is the reason why students did not summarize in time. Therefore, after the first class, I suggest my students make a mistake book and record their mistakes and cause analysis like a diary.

Generally speaking, there are three kinds of wrong questions: the first is particularly stupid mistakes, especially simple mistakes; The second is that when I got the question, I had no idea at all. I didn't know where to start solving the problem, and I suddenly realized it when I saw the answer. The third is that the difficulty of the topic is moderate, and it is reasonable to do it right, but it is wrong.

Especially the second and third kinds, you must have put the wrong books. The advantage of establishing a wrong problem book is to master the types of mistakes you have made and prevent a mistake from becoming habitual thinking.

Fourthly, graphic reasoning is the best tool to cultivate logical thinking ability.

False is true and false, true is false and true; Logical thinking is thinking under the rule, and it belongs to unconventional thinking if it is connected with life. Everything seems to have nothing to do with life, but in fact it is within the scope of laws and regulations. The "crossing the sea from the sky" of logical reasoning can be described as varied, like a kaleidoscope, with endless changes and endless fun.

Geometry is a good tool to help them exercise their logical thinking, and the classic graphic reasoning questions always have their ideas, ideas and ingenious thinking; The classic is seemingly abnormal, and the actual solution is simple and clear.

Therefore, it is very helpful for his logical thinking to train more graphic reasoning questions.